L∞ boundedness of the solutions to the Schrödinger equation on noncompact Riemannian manifolds

We are interested in the boundedness of the solutions to a Schrödinger type equation, with an integrable, sign changing potential. The sufficient condition for the boundedness relies on the integrability of a function involving both the isocapacitary function of the domain and the decreasing rearrangement of the negative part of the potential.